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Graph Translation

Graph Translation. This is a basic tutorial on how graphs are translated by various terms in the equation. James S Jun 2010. y = x 3 + 3. y = x 3. The “ + 3 ” added to x 3 adds 3 to every point on the graph and thus moves the whole graph upward. This is true of any shape graph.

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Graph Translation

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  1. Graph Translation This is a basic tutorial on how graphs are translated by various terms in the equation James S Jun 2010

  2. y = x3+ 3 y = x3 The “+ 3” added to x3 adds 3 to every point on the graph and thus moves the whole graph upward. This is true of any shape graph

  3. Graph shape is not important to translation y = x +3

  4. y = x2+ 3

  5. y = ln (x) +3

  6. In this equation, there is a horizontal shift due to the – 3 inside the parentheses and a vertical shift due to the + 3 outside the parentheses. y = (x – 3)3+ 3 y = (x)3

  7. The combination of horizontal and vertical is a diagonal shift. y = (x - 3)3+ 3 y = x3

  8. Shape of the curve in not important. y = (x – 3)2+ 3

  9. Shifted right and down y = (x – 3)2– 3

  10. y = (x + 3)2– 3 Shifted left and down

  11. y = ln (x – 3) + 3 Shifted right and up

  12. In any equation in the form: y = (x ± h)c ± k, the “h” inside the parens will shift the graph horizontally, and the “k” outside the parens will shift the graph vertically. + h shifts left, – h shifts right + k shifts upward, – k shifts downward James S Jun 2010

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